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A central limit theorem for the isotropic random sphere

Part of: Limit theorems Stochastic processes Distribution theory

Published online by Cambridge University Press:  01 July 2016

Jason J. Brown
Jason J. Brown*
Affiliation:
University of Missouri—Columbia
*
* Postal address: 5825 Saddle Seat Drive, Raleigh, NC 27606, USA.
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Abstract

Let be a real-valued, homogeneous, and isotropic random field indexed in . When restricted to those indices with , the Euclidean length of , equal to r (a positive constant), then the random field resides on the surface of a sphere of radius r. Using a modified stratified spherical sampling plan (Brown (1993)) on the sphere, define to be a realization of the random process and to be the cardinality of . Without specifying the dependence structure of nor the marginal distribution of the , conditions for asymptotic normality of the standardized sample mean, , are given. The conditions on and are motivated by the ideas and results for dependent stationary sequences.

Keywords

ISOTROPIC RANDOM FIELDSPHERE

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 642 - 651
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This research was partially supported by NSF grant DMS-94.04130.

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